College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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All the questions, please.
Part a, b, c
![### Vectors and Cross Products
#### Vectors Definition
- Vector **\(\vec{A}\)** is defined as:
\[
\vec{A} = 2\hat{i} + 3\hat{j}
\]
- Vector **\(\vec{B}\)** is defined as:
\[
\vec{B} = 2\hat{i} - 6\hat{j} + 2\hat{k}
\]
#### Problem Breakdown
##### Part A:
- **Task:** Determine the x-component of the cross product \(\vec{A} \times \vec{B}\).
- **Instructions:** Express your answer as an integer.
- **Input Box:** Placeholder for solution entry.
- **Hint Option:** View available hints if needed.
- **Submit Button:** Confirm your answer entry.
##### Part B:
- **Task:** Determine the y-component of the cross product \(\vec{A} \times \vec{B}\).
- **Instructions:** Express your answer as an integer.
- **Input Box:** Placeholder for solution entry.
- **Hint Option:** View available hints if needed.
- **Submit Button:** Confirm your answer entry.
##### Part C:
- **Task:** Determine the z-component of the cross product \(\vec{A} \times \vec{B}\).
- **Instructions:** Express your answer as an integer.
- **Input Box:** Placeholder for solution entry.
- **Hint Option:** View available hints if needed.
- **Submit Button:** Confirm your answer entry.
### Steps to Solve Cross Product
The cross product \(\vec{A} \times \vec{B}\) of two vectors \(\vec{A} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}\) and \(\vec{B} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}\) is calculated as:
\[
\vec{A} \times \vec{B} =
\begin{vmatrix}
\hat{i} & \hat{j} & \hat{k} \\
a_1 & a_2 & a_3 \\
b_1 & b_2 & b_3
\end{vmatrix}
\]
\[
= \hat{i}(a_2b](https://content.bartleby.com/qna-images/question/3d1ce009-23a3-40ae-97d8-37e468e90451/0800991f-4623-428d-b644-44ec4106cce9/st79eh9_processed.png)
Transcribed Image Text:### Vectors and Cross Products
#### Vectors Definition
- Vector **\(\vec{A}\)** is defined as:
\[
\vec{A} = 2\hat{i} + 3\hat{j}
\]
- Vector **\(\vec{B}\)** is defined as:
\[
\vec{B} = 2\hat{i} - 6\hat{j} + 2\hat{k}
\]
#### Problem Breakdown
##### Part A:
- **Task:** Determine the x-component of the cross product \(\vec{A} \times \vec{B}\).
- **Instructions:** Express your answer as an integer.
- **Input Box:** Placeholder for solution entry.
- **Hint Option:** View available hints if needed.
- **Submit Button:** Confirm your answer entry.
##### Part B:
- **Task:** Determine the y-component of the cross product \(\vec{A} \times \vec{B}\).
- **Instructions:** Express your answer as an integer.
- **Input Box:** Placeholder for solution entry.
- **Hint Option:** View available hints if needed.
- **Submit Button:** Confirm your answer entry.
##### Part C:
- **Task:** Determine the z-component of the cross product \(\vec{A} \times \vec{B}\).
- **Instructions:** Express your answer as an integer.
- **Input Box:** Placeholder for solution entry.
- **Hint Option:** View available hints if needed.
- **Submit Button:** Confirm your answer entry.
### Steps to Solve Cross Product
The cross product \(\vec{A} \times \vec{B}\) of two vectors \(\vec{A} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}\) and \(\vec{B} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}\) is calculated as:
\[
\vec{A} \times \vec{B} =
\begin{vmatrix}
\hat{i} & \hat{j} & \hat{k} \\
a_1 & a_2 & a_3 \\
b_1 & b_2 & b_3
\end{vmatrix}
\]
\[
= \hat{i}(a_2b
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